Principal filters of some ordered $\Gamma$-semigroups
For an intra-regular or a left regular and left duo ordered $\Gamma$-semigroup $M$, we describe the principal filter of $M$ which plays an essential role in the structure of this type of $po$-$\Gamma$-semigroups. We also prove that an ordered $\Gamma$-semigroup $M$ is intra-regular if and only if t...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Republic of Armenia National Academy of Sciences
2016-12-01
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| Series: | Armenian Journal of Mathematics |
| Online Access: | http://test.armjmath.sci.am/index.php/ajm/article/view/127 |
| Summary: | For an intra-regular or a left regular and left duo ordered $\Gamma$-semigroup $M$, we describe the principal filter of $M$ which plays an essential role in the structure of this type of $po$-$\Gamma$-semigroups. We also prove that an ordered $\Gamma$-semigroup $M$ is intra-regular if and only if the ideals of $M$ are semiprime and it is left (right) regular and left (right) duo if and only if the left (right) ideals of $M$ are semiprime.
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| ISSN: | 1829-1163 |